Transformation Groups ( IF 0.4 ) Pub Date : 2021-05-12 , DOI: 10.1007/s00031-021-09655-y SIDDHARTHA SAHI , HADI SALMASIAN , VERA SERGANOVA
Let (V, ω) be an orthosymplectic ℤ2-graded vector space and let 𝔤:= 𝔤𝔬𝔰𝔭 (V, ω) denote the Lie superalgebra of similitudes of (V, ω). It is known that as a 𝔤-module, the space
We also transcend our results on the eigenvalues of Capelli operators to the Deligne category Rep (Ot). More precisely, we define categorical Capelli operators \( {\left\{{D}_{t,\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \) that induce morphisms of indecomposable components of symmetric powers of Vt, where Vt is the generating object of Rep (Ot). We obtain formulas for the eigenvalue polynomials associated to the \( {\left\{{D}_{t,\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \) that are analogous to our results for the operators \( {\left\{{D}_{\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \).
中文翻译:
球超谐函数的Capelli算子和Dougall-Ramanujan身份
设(V,ω)是orthosymplecticℤ 2 -graded矢量空间和让𝔤:=𝔤𝔬𝔰𝔭(V,ω)表示的(similitudes的李代数V,ω)。众所周知,空间是𝔤模块
我们还将Capelli算子的特征值的结果超越到Deligne类别Rep(O t)。更精确地,我们定义分类卡佩里运营商\({\左\ {{d} _ {T,\ leftthreetimes} \右\}} _ {\ leftthreetimes \在\ mathcal【T}} \)诱导不可分解部件的态射的对称幂V t,其中V t是Rep(O t)的生成对象。我们获得与\({\ left \ {{D} _ {t,\ leftthreetimes} \ right \}} _ {\ leftthreetimes \ in \ mathcal {T}} \)相关的特征值多项式的公式类似于我们为运营商提供的结果\({\ left \ {{D} _ {\ leftthreetimes} \ right \}} _ {\ leftthreetimes \ in \ mathcal {T}} \\)。